Problem: $f(x) = \dfrac{ x + 6 }{ ( x + 6 )( x - 9 ) }$ What is the domain of the real-valued function $f(x)$ ?
$f(x)$ is undefined when the denominator is 0. The denominator is 0 when $x=-6$ or $x=9$ So we know that $x \neq -6$ and $x \neq 9$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid x \neq-6, \,x \neq9\, \}$.